A 13-digit ISBN, 978-3-16-148410-0, as represented by an EAN-13 bar code.

The International Standard Book Number (ISBN) is a unique^[1][2] numeric commercial book identifier based upon the 9-digit Standard Book Numbering (SBN) code created by Gordon Foster, Emeritus Professor of Statistics at Trinity College, Dublin,^[3] for the booksellers and stationers W. H. Smith and others in 1966.^[4]

The 10-digit ISBN format was developed by the International Organization for Standardization (ISO) and was published in 1970 as international standard ISO 2108.^[4] (However, the 9-digit SBN code was used in the United Kingdom until 1974.) An SBN may be converted to an ISBN by prepending the digit '0'. Currently, the ISO's TC 46/SC 9 is responsible for the ISBN. The ISO on-line facility only refers back to 1978.^[5]

Since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland EAN-13s.^[6]

Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure; however, this can be rectified later.^[7]

A similar numeric identifier, the International Standard Serial Number (ISSN), identifies periodical publications such as magazines.

Overview[link]

An ISBN is assigned to each edition and variation (except reprintings) of a book.^[8] The ISBN is 13 digits long if assigned after January 1, 2007, and 10 digits long if assigned before 2007. An International Standard Book Number consists of 4 or 5 parts:

The parts of a 10-digit ISBN and the corresponding EAN‑13 and barcode. Note the different check digits in each. The part of the EAN‑13 labeled "EAN" is the Bookland country code.

1. for a 13-digit ISBN, a GS1 prefix: 978 or 979 (indicating the industry; in this case, 978 denotes book publishing)^[9]
2. the group identifier, (language-sharing country group)^[10]
3. the publisher code,^[11]
4. the item number (title of the book),^[11] and
5. a checksum character or check digit.^[11]

The ISBN separates its parts (group, publisher, title and check digit) with either a hyphen or a space. Other than the check digit, no part of the ISBN will have a fixed number of digits.^[12]

ISBN issuance[link]

International Standard Book Numbers issuance is country specific, and is tailored for each country's national goals. In Canada the stated purpose of issuing International Standard Book Numbers for no cost was to encourage Canadian culture. In the United Kingdom and United States apparently the issuing of International Standard Book Numbers has become a profit center for the companies involved. Whether or not any of the profits accrue to the taxpayers is not known.

Australia: In Australia ISBNs are issued by the commercial library services agency Thorpe-Bowker, and prices range from $A40 for a single ISBN (plus a $A55 registration fee for new publishers) through to $2,750 for a block of 1,000 ISBNs.^[13]

Canada: In Canada Library and Archives Canada, a government agency, is the responsible entity, and there is no cost.

United Kingdom and Ireland: In the United Kingdom and Ireland the privately held company, Nielsen Book Services, part of Nielsen Holdings N.V., is the responsible entity, and there is a charge. ISBNs are sold in lots of ten or more.

United States: In the United States the privately held company R. R. Bowker is the responsible entity, and there is a charge, which varies depending upon the number of ISBNs purchased, with prices ranging from $125.00 for a single number.^[14]

Publishers and authors in other countries need to obtain ISBNs from their local ISBN Agency. A directory of ISBN Agencies is available on the International ISBN Agency website.

Group identifier[link]

The group identifier is a 1 to 5 digit number. The single digit group identifiers are: 0 or 1 for English-speaking countries; 2 for French-speaking countries; 3 for German-speaking countries; 4 for Japan; 5 for Russian-speaking countries, 7 for People's Republic of China. An example 5 digit group identifier is 99936, for Bhutan. The allocated group IDs are: 0–5, 600–617, 7, 80–94, 950–989, 9927–9989, and 99901–99967.^[15] Some catalogs include books that were published with no ISBN but add a non-standard number with an as-yet unallocated 5-digit group such as 99985; this practice is not part of the standard. Books published in rare languages typically have longer group identifiers.^[9]

The original standard book number (SBN) had no group identifier, but affixing a zero (0) as prefix to a 9-digit SBN creates a valid 10-digit ISBN. Group identifiers form a prefix code; compare with country calling codes.

Publisher code[link]

The national ISBN agency assigns the publisher number (cf. the category:ISBN agencies); the publisher selects the item number. Generally, a book publisher is not required to assign an ISBN, nor is it necessary for a book to display its number (except in China; see below). However, most book stores only handle ISBN-bearing merchandise.

A listing of all the 628,000 assigned publisher codes is published, and can be ordered in book form (€558, US$915.46). The web site of the ISBN agency does not offer any free method of looking up publisher codes.^[16] Partial lists have been compiled (from library catalogs) for the English-language groups: identifier 0 and identifier 1.

Publishers receive blocks of ISBNs, with larger blocks allotted to publishers expecting to need them; a small publisher may receive ISBNs of one or more digits for the group identifier code, several digits for the publisher, and a single digit for the individual items. Once that block of ISBNs is used, the publisher may receive another block of ISBNs, with a different publisher number. Consequently, a publisher may have different allotted publisher numbers. There also may be more than one group identifier used in a country. This might occur if a popular identifier has used up all of its numbers. The cited list of identifiers shows this has happened in China and in more than a dozen other countries.

By using variable block lengths, a large publisher will have few digits allocated for the publisher number and many digits allocated for titles; likewise countries publishing much will have few allocated digits for the group identifier, and many for the publishers and titles.^[17] Here are some sample ISBN-10 codes, illustrating block length variations.

ISBN	Country or area	Publisher
99921-58-10-7	Qatar	NCCAH, Doha
9971-5-0210-0	Singapore	World Scientific
960-425-059-0	Greece	Sigma Publications
80-902734-1-6	Czech Republic; Slovakia	Taita Publishers
85-359-0277-5	Brazil	Companhia das Letras
1-84356-028-3	English-speaking area	Simon Wallenberg Press
0-684-84328-5	English-speaking area	Scribner
0-8044-2957-X	English-speaking area	Frederick Ungar
0-85131-041-9	English-speaking area	J. A. Allen & Co.
0-943396-04-2	English-speaking area	Willmann–Bell
0-9752298-0-X	English-speaking area	KT Publishing

Pattern[link]

English-language publisher codes follow a systematic pattern, which allows their length to be easily determined, as follows:^[18]

Check digits[link]

A check digit is a form of redundancy check used for error detection, the decimal equivalent of a binary checksum. It consists of a single digit computed from the other digits in the message.

ISBN-10[link]

The 2001 edition of the official manual of the International ISBN Agency says that the ISBN-10 check digit^[19] – which is the last digit of the ten-digit ISBN – must range from 0 to 10 (the symbol X is used instead of 10) and must be such that the sum of all the ten digits, each multiplied by the integer weight, descending from 10 to 1, is a multiple of the number 11. Modular arithmetic is convenient for calculating the check digit using modulus 11. Each of the first nine digits of the ten-digit ISBN – excluding the check digit, itself – is multiplied by a number in a sequence from 10 to 2, and the remainder of the sum, with respect to 11, is computed. The resulting remainder, plus the check digit, must equal 11; therefore, the check digit is 11 minus the remainder of the sum of the products.

For example, the check digit for an ISBN-10 of 0-306-40615-? is calculated as follows:

Failed to parse (Missing texvc executable; please see math/README to configure.): \begin{align} s &= (0\times 10) + (3\times 9) + (0\times 8) + (6\times 7) + (4\times 6) + (0\times 5) + (6\times 4) + (1\times 3) + (5\times 2) \\ &= 0 + 27 + 0 + 42 + 24 + 0 + 24 + 3 + 10 \\ &= 130 = 11\times 11 + 9 \end{align}

Thus the remainder is 9, the check digit is 2, and the complete sequence is ISBN 0-306-40615-2.

Formally, the check digit calculation is:

Failed to parse (Missing texvc executable; please see math/README to configure.): (10x_1 + 9x_2 + 8x_3 + 7x_4 + 6x_5 + 5x_6 + 4x_7 + 3x_8 + 2x_9 + x_{10})\mod{11} \equiv 0.

The value Failed to parse (Missing texvc executable; please see math/README to configure.): x_{10}

required to satisfy this condition might be 10; if so, an 'X' should be used.

The two most common errors in handling an ISBN (e.g., typing or writing it) are an altered digit or the transposition of adjacent digits. The ISBN check digit method ensures that these two errors will always be detected. However, if the error occurs in the publishing house and goes undetected, the book will be issued with an invalid ISBN.^[20]

Alternative calculation[link]

The simplest way to verify an ISBN is to compute a sum of the digits of the ISBN: <source lang="cpp"> // C++ bool is_isbn_valid(char digits[10]) {

   int i, a = 0, b = 0;
   for (i = 0; i < 10; i++) {
       a += digits[i];  // Assumed already converted from ASCII to 0..9
       b += a;
   }
   return b % 11 == 0;

} </source>

The ISBN-10 check-digit can also be calculated in a slightly easier way:

Failed to parse (Missing texvc executable; please see math/README to configure.): x_{10} = ( 1x_1 + 2x_2 + 3x_3 + 4x_4 + 5x_5 + 6x_6 + 7x_7 +8x_8 + 9x_9 )\, \bmod\;11.

This is simply replacing 11 with 0, and each subtraction with its complement: Failed to parse (Missing texvc executable; please see math/README to configure.): -10 \equiv 1 \mod 11,

etc.

For example, the check digit for an ISBN-10 of 0-306-40615-? is calculated as follows:

Failed to parse (Missing texvc executable; please see math/README to configure.): (1 \times 0 + 2 \times 3 + 3 \times 0 + 4 \times 6 + 5 \times 4 + 6 \times 0 + 7 \times 6 + 8 \times 1 + 9 \times 5) \, \bmod\; 11 = 145 \, \bmod\; 11 = 2

ISBN-13[link]

The 2005 edition of the International ISBN Agency's official manual^[21] covering some ISBNs issued from January 2007, describes how the 13-digit ISBN check digit is calculated.

The calculation of an ISBN-13 check digit begins with the first 12 digits of the thirteen-digit ISBN (thus excluding the check digit itself). Each digit, from left to right, is alternately multiplied by 1 or 3, then those products are summed modulo 10 to give a value ranging from 0 to 9. Subtracted from 10, that leaves a result from 1 to 10. A zero (0) replaces a ten (10), so, in all cases, a single check digit results.

For example, the ISBN-13 check digit of 978-0-306-40615-? is calculated as follows:

s = 9×1 + 7×3 + 8×1 + 0×3 + 3×1 + 0×3 + 6×1 + 4×3 + 0×1 + 6×3 + 1×1 + 5×3
  =   9 +  21 +   8 +   0 +   3 +   0 +   6 +  12 +   0 +  18 +   1 +  15
  = 93
93 / 10 = 9 remainder 3
10 –  3 = 7

Thus, the check digit is 7, and the complete sequence is ISBN 978-0-306-40615-7.

Formally, the ISBN-13 check digit calculation is:

Failed to parse (Missing texvc executable; please see math/README to configure.): x_{13} = \big(10 - \big(x_1 + 3x_2 + x_3 + 3x_4 + \cdots + x_{11} + 3x_{12}\big) \,\bmod\, 10\big) \,\bmod\, 10.

This check system – similar to the UPC check digit formula – does not catch all errors of adjacent digit transposition. Specifically, if the difference between two adjacent digits is 5, the check digit will not catch their transposition. For instance, the above example allows this situation with the 6 followed by a 1. The correct order contributes 3×6+1×1 = 19 to the sum; while, if the digits are transposed (1 followed by a 6), the contribution of those two digits will be 3×1+1×6 = 9. However, 19 and 9 are congruent modulo 10, and so produce the same, final result: both ISBNs will have a check digit of 7. The ISBN-10 formula uses the prime modulus 11 which avoids this blind spot, but requires more than the digits 0-9 to express the check digit.

Additionally, If you triple the sum of the 2nd, 4th, 6th, 8th, 10th, and 12th digits and then add them to the remaining digits (1st, 3rd, 5th, 7th, 9th, 11th, and 13th), the total will always be divisible by 10 (i.e., end in 0).

<source lang="java"> // Java public static boolean isISBN13Valid(String isbn) {

   int check = 0;
   for (int i = 0; i < 12; i += 2) {
       check += Integer.valueOf(isbn.substring(i, i + 1));
   }
   for (int i = 1; i < 12; i += 2) {
       check += Integer.valueOf(isbn.substring(i, i + 1)) * 3;
   }
   check += Integer.valueOf(isbn.substring(12));
   return check % 10 == 0;

} </source>

<source lang="php"> //PHP function is_isbn_13_valid($n){

   $check = 0;
   for ($i = 0; $i < 13; $i+=2) $check += substr($n, $i, 1);
   for ($i = 1; $i < 12; $i+=2) $check += 3 * substr($n, $i, 1);
   return $check % 10 == 0;

}</source> <source lang="ruby">

1. Ruby

def is_valid_isbn13?(isbn13)

 sum = 0
 13.times { |i| sum += i.modulo(2)==0 ? isbn13[i].to_i : isbn13[i].to_i*3 }
 0 == sum.modulo(10)

end

def isbn13_checksum(isbn12)

 sum = 0
 12.times { |i| sum += i.modulo(2)==0 ? isbn12[i].to_i : isbn12[i].to_i*3 }
 10 - sum.modulo(10)

end</source>

<source lang="python">

1. Python

def is_valid_isbn13(isbn13):

   total = sum([int(num)*weight for num, weight in zip(isbn13, (1,3)*6)])
   ck = 10-(total%10)
   return ck == int(isbn13[-1])

</source>

<source lang="cpp">

1. C/C++

bool is_valid_isbn13(char digits[13]) { int i, check=0; for (i=0; i<13; i+=2) check += digits[i]; for (i=1; i<12; i+=2) check += 3*digits[i]; return check%10==0; } </source>

Errors in usage[link]

Publishers and libraries have varied policies about the use of the ISBN check digit. Publishers sometimes fail to check the correspondence of a book title and its ISBN before publishing it; that failure causes book identification problems for libraries, booksellers, and readers.^[22]

Most libraries and booksellers display the book record for an invalid ISBN issued by the publisher. The Library of Congress catalogue contains books published with invalid ISBNs, which it usually tags with the phrase "Cancelled ISBN".^[23] However, book-ordering systems such as Amazon.com will not search for a book if an invalid ISBN is entered to its search engine.^{[citation needed]}

EAN format used in barcodes, and upgrading[link]

Currently the barcodes on a book's back cover (or inside a mass-market paperback book's front cover) are EAN-13; they may have a separate barcode encoding five digits for the currency and the recommended retail price.^[24] The number "978", the Bookland "country code", is prefixed to the ISBN in the barcode data, and the check digit is recalculated according to the EAN13 formula (modulo 10, 1x and 3x weighting on alternate digits).

Partly because of an expected shortage in certain ISBN categories, the International Organization for Standardization (ISO) decided to migrate to a thirteen-digit ISBN (ISBN-13). The process began January 1, 2005 and was planned to conclude January 1, 2007.^[25] As of 2011, all the 13-digit ISBNs begin with 978. As the 978 ISBN supply is exhausted, the 979 prefix will be introduced. This is expected to occur more rapidly outside the United States. Originally, 979 was the Musicland code for musical scores with an ISMN. However, ISMN codes will differ visually as they begin with an "M" letter; the bar code represents the "M" as a zero (0), and for checksum purposes it will count as a 3.

Publisher identification code numbers are unlikely to be the same in the 978 and 979 ISBNs, likewise, there is no guarantee that language area code numbers will be the same. Moreover, the ten-digit ISBN check digit generally is not the same as the thirteen-digit ISBN check digit. Because the EAN/UCC-13 is part of the Global Trade Item Number (GTIN) system (that includes the EAN/UCC-14, the UPC-12, and the EAN-8), it is expected that ISBN-generating software should accommodate fourteen-digit ISBNs.^[26]

Barcode format compatibility is maintained, because (aside from the group breaks) the ISBN-13 barcode format is identical to the EAN barcode format of existing ISBN-10s. So, migration to an EAN-based system allows booksellers the use of a single numbering system for both books and non-book products that is compatible with existing ISBN-based data, with only minimal changes to information technology systems. Hence, many booksellers (e.g., Barnes & Noble) migrated to EAN barcodes as early as March 2005. Although many American and Canadian booksellers were able to read EAN-13 barcodes before 2005, most general retailers could not read them. The upgrading of the UPC barcode system to full EAN-13, in 2005, eased migration to the ISBN-13 in North America. Moreover, by January 2007, most large book publishers added ISBN-13 barcodes alongside the ten-digit ISBN barcodes of books published before January 2007.^[27]

See also[link]

• ASIN (Amazon Standard Identification Number)
• CODEN (serial publication identifier currently used by libraries; replaced by the ISSN for new works)
• DOI (Digital Object Identifier)
• ESTC (English Short Title Catalogue)
• ETTN (Electronic Textbook Track Number)
• ISAN (International Standard Audiovisual Number)
• ISMN (International Standard Music Number)
• ISWC (International Standard Musical Work Code)
• ISRC (International Standard Recording Code)
• ISSN (International Standard Serial Number)
• ISWN (International Standard Wine Number)
• LCCN (Library of Congress Control Number)
• List of group-0 ISBN publisher codes
• List of group-1 ISBN publisher codes
• OCLC number (Online Computer Library Center number [1])
• Registration authority
• SICI (Serial Item and Contribution Identifier)
• Special:Booksources, Wikipedia's ISBN search page
• VD 16 (Verzeichnis der im deutschen Sprachbereich erschienenen Drucke des 16. Jahrhunderts)(in English: Bibliography of Books Printed in the German Speaking Countries of the Sixteenth Century)
• VD 17 (Verzeichnis der im deutschen Sprachraum erschienenen Drucke des 17. Jahrhunderts)(in English: Bibliography of Books Printed in the German Speaking Countries of the Seventeenth Century)

Notes[link]

External links[link]

• ISO 2108:2005 at www.iso.org
• ISBN to EAN EAS^{[disambiguation needed ]} EBS^{[disambiguation needed ]} transition at isbn.org
• Description of the ISBN to EAN upgrade process at bookweb.org
• International ISBN Agency—coordinates and supervises the worldwide use of the ISBN system.
• Numerical List of Group Identifiers List of language/region prefixes
• Free conversion tool: ISBN-10 to ISBN-13 & ISBN-13 to ISBN-10 from the ISBN agency. Also shows correct hyphenation & verifies if ISBNs are valid or not.
• RFC 3187 Using International Standard Book Numbers as Uniform Resource Names (URN)
• Implementation guidelinesPDF (51.0 KB) for the 13-digit ISBN code.

John David Barrow FRS (born 29 November 1952, London) is an English cosmologist, theoretical physicist, and mathematician. He is currently Research Professor of Mathematical Sciences at the University of Cambridge. Barrow is also a writer of popular science and an amateur playwright.

Life[link]

Barrow obtained his first degree in mathematics and physics from Van Mildert College at the University of Durham in 1974.^[1] In 1977, he completed his doctorate in astrophysics at Magdalen College in the University of Oxford under Dennis William Sciama. He did two postdoctoral years in astronomy at the University of California, Berkeley.

In 1981 he joined the University of Sussex and rose to the rank of Professor. In 1999, he became Professor in the Department of Applied Mathematics and Theoretical Physics and a fellow in Clare Hall at Cambridge University. He is Director of the Millennium Mathematics Project. From 2003–2007 he was Gresham Professor of Astronomy at Gresham College, London, and he has been appointed as Gresham Professor of Geometry from 2008–2011; only one person has previously held two different Gresham chairs.^[2] In 2008, the Royal Society awarded him the Faraday Prize.

In addition to having published more than 400 journal articles, Barrow has coauthored (with Frank J. Tipler) The Anthropic Cosmological Principle, a work on the history of the ideas, specifically intelligent design and teleology, as well as a treatise on astrophysics. He has also published 17 books for general readers, beginning with his 1983 The Left Hand of Creation. His books summarise the state of the affairs of physical questions, often in the form of compendia of a large number of facts assembled from the works of great physicists, such as Paul Dirac and Arthur Eddington.

Barrow's approach to philosophical issues posed by physical cosmology makes his books accessible to general readers. For example, Barrow introduced a memorable paradox, which he called "the Groucho Marx Effect" (see Russell-like paradoxes). Here, he quotes Groucho Marx: "I wouldn't want to belong to any club that would accept me as a member". Applying this to problems in cosmology, Barrow states: "A universe simple enough to be understood is too simple to produce a mind capable of understanding it."^[3] That is, the better we understand the problem, the more likely it is to be oversimplified. Conversely, the closer we get to a description of reality, the more complex and incomprehensible the description becomes. There would be few if any fields of study in which this paradox does not apply.

Barrow has lectured at 10 Downing Street, Windsor Castle, the Vatican, and to the general public. In 2002, his play Infinities premiered in Milan, played in Valencia, and won the Premi Ubu 2002 Italian Theatre Prize.

He was awarded the 2006 Templeton Prize for "Progress Toward Research or Discoveries about Spiritual Realities" for his "writings about the relationship between life and the universe, and the nature of human understanding [which] have created new perspectives on questions of ultimate concern to science and religion".^[4] He is a member of a United Reformed Church, which he describes as teaching "a traditional deistic picture of the universe".^[5]

Books[link]

In English:

1. Cosmic Imagery: Key Images in the History of Science. ISBN 978-0224075237
2. New Theories of Everything. ISBN 978-0192807212
3. Between Inner Space and Outer Space: Essays on the Science, Art, and Philosophy of the Origin of the Universe
4. Impossibility: Limits of Science and the Science of Limits. ISBN 0-09-977211-6
5. Material Content of the Universe
6. Pi in the Sky: Counting, Thinking, and Being
7. Science and Ultimate Reality: Quantum Theory, Cosmology and Complexity
8. ^{[Edit this reference]}
   Barrow, John D.; Tipler, Frank J. (19 May 1988). The Anthropic Cosmological Principle. foreword by John A. Wheeler. Oxford: Oxford University Press. ISBN 9780192821478. LC 87-28148. http://books.google.com/books?id=uSykSbXklWEC&printsec=frontcover. Retrieved 31 December 2009. 
9. The Artful Universe: The Cosmic Source of Human Creativity
10. The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe
11. The Infinite Book: A Short Guide to the Boundless, Timeless and Endless
12. The Left Hand of Creation: The Origin and Evolution of the Expanding Universe
13. The Origin of the Universe: To the Edge of Space and Time
14. The Universe That Discovered Itself
15. The World Within the World
16. Theories of Everything: The Quest for Ultimate Explanation
17. The Constants of Nature: The Numbers that Encode the Deepest Secrets of the Universe
18. 100 Essential Things You Didn't Know You Didn't Know

In other languages:

1. L'Homme et le Cosmos (in French)
2. Perché il Mondo è Matematico? (in Italian)

See also[link]

• Anthropic principle
• Final anthropic principle
• Cornucopian

References[link]

External links[link]

• John D Barrow homepage
• John D Barrow (updated) homepage
• Publications list
• Millennium Mathematics Project
• Barrow's math genealogy
• Audio: John D. Barow in conversation on the BBC World Service discussion show The Forum

Publications available on the Internet[link]

• Chaos in Numberland: the secret life of continued fractions
• Chaos
• Mathematics and Sports
• Connections in Space website and CD Rom on mathematical and artistic aspects of space, with R. Bright, M. Kemp i N. Mee
• Outer space - A Sense of Balance
• Living in a Simulation, 2003.
• Outer Space - Independence Day
• Solution to A Sense of Balance
• Outer Space - Rugby and Relativity
• Solution to Independence Day
• Wagons Roll
• Solution to Rugby and Relativity